Make sure that Abbreviate Cut Time to is checked. Also, change the character to use for cut time to the Common Time symbol. Normaly, you should enter c in that entry box (instead of C).

Now you can use both 4/4 and Common Time. To display common time, use the time signature of 2/2.

Second method can be used in any document:

Go to the Options/Document Settings/Time Signature Options... dialog box. Make sure that Abbreviate Common Time to is checked. Close the dialog box.

When you later want 4/4 instead of the default Common Time, click on the Options >> button to expand the time signature dialog. Check Use a Different Time Signature for Display and uncheck Abbreviate. 4/4 will now show up instead of Common Time.